title: Two-component Dirac-like Hamiltonian for generating quantum walk on one-, two- and three-dimensional lattices.
abstract: From the unitary operator used for implementing two-state discrete-time quantum walk on one-, two- and three- dimensional lattice we obtain a two-component Dirac-like Hamiltonian. In particular, using different pairs of Pauli basis as position translation states we obtain three different form of Hamiltonians for evolution on one-dimensional lattice. We extend this to two- and three-dimensional lattices using different Pauli basis states as position translation states for each dimension and show that the external coin operation, which is necessary for one-dimensional walk is not a necessary requirement for a walk on higher dimensions but can serve as an additional resource to control the dynamics. The two-component Hamiltonian we present here for quantum walk on different lattices can serve as a general framework to simulate, control, and study the dynamics of quantum systems governed by Dirac-like Hamiltonian.
authors.affiliation: Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, Okinawa, Japan.
authors.forename: C M
authors.initials: CM
authors.lastname: Chandrashekar